{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "305bd118",
   "metadata": {},
   "source": [
    "# Optional Lab: Logistic Regression, Logistic Loss\n",
    "\n",
    "In this ungraded lab, you will:\n",
    "- explore the reason the squared error loss is not appropriate for logistic regression\n",
    "- explore the logistic loss function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cd12f75d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:16:07.836322Z",
     "start_time": "2022-06-17T12:16:06.310530Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "%matplotlib widget\n",
    "import matplotlib.pyplot as plt\n",
    "from plt_logistic_loss import  plt_logistic_cost, plt_two_logistic_loss_curves, plt_simple_example\n",
    "from plt_logistic_loss import soup_bowl, plt_logistic_squared_error\n",
    "plt.style.use('./deeplearning.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5537d5a5",
   "metadata": {},
   "source": [
    "## Squared error for logistic regression?\n",
    "<img align=\"left\" src=\"../work/images/C1_W3_SqErrorVsLogistic.png\"     style=\" width:400px; padding: 10px; \" > Recall for **Linear** Regression we have used the **squared error cost function**:\n",
    "The equation for the squared error cost with one variable is:\n",
    "  $$J(w,b) = \\frac{1}{2m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)})^2 \\tag{1}$$ \n",
    " \n",
    "where \n",
    "  $$f_{w,b}(x^{(i)}) = wx^{(i)} + b \\tag{2}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f725a18c",
   "metadata": {},
   "source": [
    "Recall, the squared error cost had the nice property that following the derivative of the cost leads to the minimum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c91a57b5",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:16:09.308320Z",
     "start_time": "2022-06-17T12:16:07.839306Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "soup_bowl()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76d04418",
   "metadata": {},
   "source": [
    "This cost function worked well for linear regression, it is natural to consider it for logistic regression as well. However, as the slide above points out, $f_{wb}(x)$ now has a non-linear component, the sigmoid function:   $f_{w,b}(x^{(i)}) = sigmoid(wx^{(i)} + b )$.   Let's try a squared error cost on the example from an earlier lab, now including the sigmoid.\n",
    "\n",
    "Here is our training data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3321f6d7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:16:09.560376Z",
     "start_time": "2022-06-17T12:16:09.313321Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_train = np.array([0., 1, 2, 3, 4, 5],dtype=np.longdouble)\n",
    "y_train = np.array([0,  0, 0, 1, 1, 1],dtype=np.longdouble)\n",
    "plt_simple_example(x_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec03da32",
   "metadata": {},
   "source": [
    "Now, let's get a surface plot of the cost using a *squared error cost*:\n",
    "  $$J(w,b) = \\frac{1}{2m} \\sum\\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)})^2 $$ \n",
    " \n",
    "where \n",
    "  $$f_{w,b}(x^{(i)}) = sigmoid(wx^{(i)} + b )$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3aa960a8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:16:10.608555Z",
     "start_time": "2022-06-17T12:16:09.565380Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.close('all')\n",
    "plt_logistic_squared_error(x_train,y_train)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa4356c0",
   "metadata": {},
   "source": [
    "While this produces a pretty interesting plot, the surface above not nearly as smooth as the 'soup bowl' from linear regression!    \n",
    "\n",
    "Logistic regression requires a cost function more suitable to its non-linear nature. This starts with a Loss function. This is described below."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab1e6edf",
   "metadata": {},
   "source": [
    "## Logistic Loss Function\n",
    "<img align=\"left\" src=\"../work/images/C1_W3_LogisticLoss_a.png\"     style=\" width:250px; padding: 2px; \" >\n",
    "<img align=\"left\" src=\"../work/images/C1_W3_LogisticLoss_b.png\"     style=\" width:250px; padding: 2px; \" >\n",
    "<img align=\"left\" src=\"../work/images/C1_W3_LogisticLoss_c.png\"     style=\" width:250px; padding: 2px; \" > "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24469279",
   "metadata": {},
   "source": [
    "Logistic Regression uses a loss function more suited to the task of categorization where the target is 0 or 1 rather than any number. \n",
    "\n",
    ">**Definition Note:**   In this course, these definitions are used:  \n",
    "**Loss** is a measure of the difference of a single example to its target value while the  \n",
    "**Cost** is a measure of the losses over the training set\n",
    "\n",
    "\n",
    "This is defined: \n",
    "* $loss(f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}), y^{(i)})$ is the cost for a single data point, which is:\n",
    "\n",
    "\\begin{equation}\n",
    "  loss(f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}), y^{(i)}) = \\begin{cases}\n",
    "    - \\log\\left(f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right) & \\text{if $y^{(i)}=1$}\\\\\n",
    "    \\log \\left( 1 - f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right) & \\text{if $y^{(i)}=0$}\n",
    "  \\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "*  $f_{\\mathbf{w},b}(\\mathbf{x}^{(i)})$ is the model's prediction, while $y^{(i)}$ is the target value.\n",
    "\n",
    "*  $f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) = g(\\mathbf{w} \\cdot\\mathbf{x}^{(i)}+b)$ where function $g$ is the sigmoid function.\n",
    "\n",
    "The defining feature of this loss function is the fact that it uses two separate curves. One for the case when the target is zero or ($y=0$) and another for when the target is one ($y=1$). Combined, these curves provide the behavior useful for a loss function, namely, being zero when the prediction matches the target and rapidly increasing in value as the prediction differs from the target. Consider the curves below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cefa0d51",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:16:10.986072Z",
     "start_time": "2022-06-17T12:16:10.610556Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt_two_logistic_loss_curves()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cab45625",
   "metadata": {},
   "source": [
    "Combined, the curves are similar to the quadratic curve of the squared error loss. Note, the x-axis is $f_{\\mathbf{w},b}$ which is the output of a sigmoid. The sigmoid output is strictly between 0 and 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c05a258",
   "metadata": {},
   "source": [
    "The loss function above can be rewritten to be easier to implement.\n",
    "    $$loss(f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}), y^{(i)}) = (-y^{(i)} \\log\\left(f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right) - \\left( 1 - y^{(i)}\\right) \\log \\left( 1 - f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right)$$\n",
    "  \n",
    "This is a rather formidable-looking equation. It is less daunting when you consider $y^{(i)}$ can have only two values, 0 and 1. One can then consider the equation in two pieces:  \n",
    "when $ y^{(i)} = 0$, the left-hand term is eliminated:\n",
    "$$\n",
    "\\begin{align}\n",
    "loss(f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}), 0) &= (-(0) \\log\\left(f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right) - \\left( 1 - 0\\right) \\log \\left( 1 - f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right) \\\\\n",
    "&= -\\log \\left( 1 - f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right)\n",
    "\\end{align}\n",
    "$$\n",
    "and when $ y^{(i)} = 1$, the right-hand term is eliminated:\n",
    "$$\n",
    "\\begin{align}\n",
    "  loss(f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}), 1) &=  (-(1) \\log\\left(f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right) - \\left( 1 - 1\\right) \\log \\left( 1 - f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right)\\\\\n",
    "  &=  -\\log\\left(f_{\\mathbf{w},b}\\left( \\mathbf{x}^{(i)} \\right) \\right)\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "OK, with this new logistic loss function, a cost function can be produced that incorporates the loss from all the examples. This will be the topic of the next lab. For now, let's take a look at the cost vs parameters curve for the simple example we considered above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ade21cfb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-06-17T12:16:11.965297Z",
     "start_time": "2022-06-17T12:16:10.988074Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.close('all')\n",
    "cst = plt_logistic_cost(x_train,y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07e217db",
   "metadata": {},
   "source": [
    "This curve is well suited to gradient descent! It does not have plateaus, local minima, or discontinuities. Note, it is not a bowl as in the case of squared error. Both the cost and the log of the cost are plotted to illuminate the fact that the curve, when the cost is small, has a slope and continues to decline. Reminder: you can rotate the above plots using your mouse."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed5884b5",
   "metadata": {},
   "source": [
    "## Congratulation!  \n",
    "You have:\n",
    " - determined a squared error loss function is not suitable for classification tasks\n",
    " - developed and examined the logistic loss function which **is** suitable for classification tasks.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c1d5fcea",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.13"
  },
  "toc-showcode": true
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
